Multilinear Operators Factoring through Hilbert Spaces

We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We prove that Hilbert-Schmidt and Lipschitz \(2\)-summing m...

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Bibliographic Details
Published in:arXiv.org 2018-05
Main Authors: Fernández-Unzueta, Maite, García-Hernández, Samuel
Format: Article
Language:English
Subjects:
Hilbert space
Operators
Quantum theory
Tensors
Online Access:Get full text
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Summary:We characterize those bounded multilinear operators that factor through a Hilbert space in terms of its behavior in finite sequences. This extends a result, essentially due to S. Kwapie\'{n}, from the linear to the multilinear setting. We prove that Hilbert-Schmidt and Lipschitz \(2\)-summing multilinear operators naturally factor through a Hilbert space. It is also proved that the class \(\Gamma\) of all multilinear operators that factor through a Hilbert space is a maximal multi-ideal; moreover, we give an explicit formulation of a finitely generated tensor norm \(\gamma\) which is in duality with \(\Gamma\).
ISSN:2331-8422
DOI:10.48550/arxiv.1805.09748